Everywhere I've worked over the years (35+), and in conversation with peers (outside of work), refactor means to change the structure of an existing program, while retaining all of the original functionality. With no specificity regarding how big or small such changes may amount to.

With a rewrite usually implying starting from scratch — whether small or large — replacing existing implementations (of functions/methods/modules/whatever), with newly created ones.

Indeed one can refactor a large codebase, without actually rewriting much- if anything at all- of substance.

Maybe one could claim that this is actually lots of micro-refactors — but that doesn't flow particularly well in communication — and if the sum total of it is not specifically a "rewrite", then what collective / overarching noun should be used for the sum total of the plurality of all of these smaller refactorings? — If one spent time making lots of smaller changes, but not actually re-implementing anything... to me, that's not a rewrite, the code has been refactored, even if it is a large piece of code with a lot of structural changes throughout.

Perhaps part of the issue here in this context, is that LLMs don't particularly refactor code anyhow, they generally rewrite (regenerate) it. Which is where many of the subtle issues that are described in other comments here, creep in. The kinds of issues that a human wouldn't necessarily create when refactoring (e.g. changed regex, changed dates, other changes to functionality, etc)

Yes, the incorrect usage is widespread! See Fowler's original book for the thinking behind the term -- every example therein is a 1-minute job, and many are macros in your IDE.

Good point that LLMs tend to rewrite unless corrected. I have heard (but not tested myself!) that if you tell them to apply a series of small changes they stay on track better. Fowler's list would probably be a good starting place.